7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

A new universal mechanism for the turbulent relaxation in incompressible fluidsand plasmas
Supratik Banerjee1, Arijit Halder1 and Nandita Pan1
1
Department of physics, Indian Institute of Technology Kanpur, Indiae-mail (speaker): sbanerjee@iitk.ac.in

Turbulent relaxation in cosmic plasmas is nearly aseventy-year-old problem. When the external forcing isquenched, a turbulent plasma is believed to relax to a
Beltrami-Taylor state where the magnetic field b and thecurrent j are aligned. Such alignments are alreadyobserved in the stellar envelopes, gaseous nebulae andinterstellar plasmas. Why a turbulent system attains suchan aligned state is pivotal to understand the relaxation
dynamics of fluids and plasmas. Despite several theories,
a clear unambiguous understanding of the same remains
a mystery [1]. Of all competing theories of relaxation,
the most popular one is the theory of selective decay
where such a relaxed state can be attained by minimizing
the quickly varying quantities (the target function)
keeping the slowly varying inviscid invariants asapproximately constants [2]. Similar conclusion can betheoretically drawn for the alignment between thevelocity and the vorticity fields in neutral fluids.
Interestingly, the relaxed state of an MHD plasma withmoderate beta is numerically found to be j x b = ∇p, thus
supporting a finite pressure gradient. Similar pressurebalanced relaxed states are found for the turbulent
relaxation of neutral fluids as well. Selective decay,
however, cannot account for a finite pressure gradient atrelaxed state.

According to PVNLT, the relaxed states are achieved
when the average scale-to-scale nonlinear transfer
vanishes identically at all scales in the inertial zone [3].
These relaxed states are therefore obtained to ensure anequilibrium steady state in the inertial range in theabsence of any energy input in the large scales (seeFigure 1 below). This is in consistency with theconservation of the inviscid invariants. Microscopically,such behaviour can be justified by the maximization ofan entropy function in spectral space. PVNLT
successfully captures the relaxed states supporting a
non-zero finite pressure gradient. The Beltrami-Taylor
aligned states are naturally obtained automatically in thelimit of insignificant pressure gradient or low plasmabeta. Furthermore, PVNLT also successfully determines
whether a plasma relaxes towards a force-free state (j-balignment) or to a state of dynamic alignment (v-balignment) according to the chosen initial conditions on
the helicities. The proposed theory correctly produces all
the previously obtained relaxed states in both
two-dimensional and three-dimensional fluids andplasmas. The fundamental universal nature of PVNLT
assures its applicability to more complicated systems likebinary fluids, ferrofluids, compressible fluids andplasmas.

The present work proposes a universal explanationof the turbulent relaxation of fluids and plasmas in termsof the principle of vanishing nonlinear transfer (PVNLT).

References[1] Chandrasekhar & Woltjer, Proc. Natil. Acad. Sci., 44, 285 (1958).
[2] Mahajan & Yoshida, Phys. Rev. Lett., 81, 4863 (1998)[3] Banerjee, Halder & Pan, Phys. Rev. E (Lett.), 107, L043201 (2023)

Figure 1. A schematic diagram of the Principle of Vanishing Nonlinear Transfer